The practice of statistics for ap

978 Pages·2015·63.27 MB·English

by  Daren S. Starnes

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Using The Practice of Statistics, Fifth Edition, for Advanced Placement (AP®) Statistics
(The percents in parentheses reflect coverage on the AP® exam.)
Topic Outline for AP® Statistics The Practice of Statistics, 5th ed.
from the College Board’s AP ® Statistics Course Description Chapter and Section references
I. Exploring data: describing patterns and departures from patterns (20%–30%)
A. Constructing and interpreting graphical displays of distributions of univariate data (dotplot, Dotplot, stemplot, histogram 1.2;
stemplot, histogram, cumulative frequency plot) Cumulative frequency plot 2.1
1. Center and spread 1.2
2. Clusters and gaps 1.2
3. Outliers and unusual features 1.2
4. Shape 1.2
B. Summarizing distributions of univariate data 1.3 and 2.1
1. Measuring center: median, mean 1.3
2. Measuring spread: range, interquartile range, standard deviation 1.3
3. Measuring position: quartiles, percentiles, standardized scores (z-scores) Quartiles 1.3; percentiles and z-scores 2.1
4. Using boxplots 1.3
5. The effect of changing units on summary measures 2.1
C. Comparing distributions of univariate data (dotplots, back-to-back stemplots, parallel boxplots) Dotplots and stemplots 1.2;
boxplots 1.3
1. Comparing center and spread 1.2 and 1.3
2. Comparing clusters and gaps 1.2 and 1.3
3. Comparing outliers and unusual features 1.2 and 1.3
4. Comparing shape 1.2 and 1.3
D. Exploring bivariate data Chapter 3 and Section 12.2
1. Analyzing patterns in scatterplots 3.1
2. Correlation and linearity 3.1
3. Least-squares regression line 3.2
4. Residual plots, outliers, and influential points 3.2
5. Transformations to achieve linearity: logarithmic and power transformations 12.2
E. Exploring categorical data Sections 1.1, 5.2, 5.3
1. Frequency tables and bar charts 1.1 (we call them bar graphs)
2. Marginal and joint frequencies for two-way tables Marginal 1.1; joint 5.2
3. Conditional relative frequencies and association 1.1 and 5.3
4. Comparing distributions using bar charts 1.1
II. Sampling and experimentation: planning and conducting a study (10%–15%)
A. Overview of methods of data collection Sections 4.1 and 4.2
1. Census 4.1
2. Sample survey 4.1
3. Experiment 4.2
4. Observational study 4.2
B. Planning and conducting surveys Section 4.1
1. Characteristics of a well-designed and well-conducted survey 4.1
2. Populations, samples, and random selection 4.1
3. Sources of bias in sampling and surveys 4.1
4. Sampling methods, including simple random sampling, stratified random sampling, 4.1
and cluster sampling
C. Planning and conducting experiments Section 4.2
1. Characteristics of a well-designed and well-conducted experiment 4.2
2. Treatments, control groups, experimental units, random assignments, and replication 4.2
3. Sources of bias and confounding, including placebo effect and blinding 4.2
4. Completely randomized design 4.2
5. Randomized block design, including matched pairs design 4.2
D. Generalizability of results and types of conclusions that can be drawn from Section 4.3
observational studies, experiments, and surveys
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Using The Practice of Statistics, Fifth Edition, for Advanced Placement (AP®) Statistics
(The percents in parentheses reflect coverage on the AP® exam.)
Topic Outline for AP® Statistics The Practice of Statistics, 5th ed.
from the College Board’s AP ® Statistics Course Description Chapter and Section references
III. Anticipating patterns: exploring random phenomena using probability and simulation (20%–30%)
A. Probability Chapters 5 and 6
1. Interpreting probability, including long-run relative frequency interpretation 5.1
2. “Law of large numbers” concept 5.1
3. Addition rule, multiplication rule, conditional probability, and independence Addition rule 5.2; other three topics 5.3
4. Discrete random variables and their probability distributions, including binomial and geometric Discrete 6.1; Binomial
and geometric 6.3
5. Simulation of random behavior and probability distributions 5.1
6. Mean (expected value) and standard deviation of a random variable, and linear Mean and standard deviation 6.1;
transformation of a random variable Linear transformation 6.2
B. Combining independent random variables Section 6.2
1. Notion of independence versus dependence 6.2
2. Mean and standard deviation for sums and differences of independent random variables 6.2
C. The Normal distribution Section 2.2
1. Properties of the Normal distribution 2.2
2. Using tables of the Normal distribution 2.2
3. The Normal distribution as a model for measurements 2.2
D. Sampling distributions Chapter 7; Sections 8.3,
10.1, 10.2, 11.1
1. Sampling distribution of a sample proportion 7.2
2. Sampling distribution of a sample mean 7.3
3. Central limit theorem 7.3
4. Sampling distribution of a difference between two independent sample proportions 10.1
5. Sampling distribution of a difference between two independent sample means 10.2
6. Simulation of sampling distributions 7.1
7. t distribution 8.3
8. Chi-square distribution 11.1
IV. Statistical inference: estimating population parameters and testing hypotheses (30%–40%)
A. Estimation (point estimators and confidence intervals) Chapter 8 plus parts of Sections 9.3, 10.1,
10.2, 12.1
1. Estimating population parameters and margins of error 8.1
2. Properties of point estimators, including unbiasedness and variability 8.1
3. Logic of confidence intervals, meaning of confidence level and confidence intervals, 8.1
and properties of confidence intervals
4. Large-sample confidence interval for a proportion 8.2
5. Large-sample confidence interval for a difference between two proportions 10.1
6. Confidence interval for a mean 8.3
7. Confidence interval for a difference between two means (unpaired and paired) Paired 9.3; unpaired 10.2
8. Confidence interval for the slope of a least-squares regression line 12.1
B. Tests of significance Chapters 9 and 11 plus parts of Sections
10.1, 10.2, 12.1
1. Logic of significance testing, null and alternative hypotheses; P-values; one-and two-sided tests; 9.1; power in 9.2
concepts of Type I and Type II errors; concept of power
2. Large-sample test for a proportion 9.2
3. Large-sample test for a difference between two proportions 10.1
4. Test for a mean 9.3
5. Test for a difference between two means (unpaired and paired) Paired 9.3; unpaired 10.2
6. Chi-square test for goodness of fit, homogeneity of proportions, and independence Chapter 11
(one- and two-way tables)
7. Test for the slope of a least-squares regression line 12.1
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For the AP® Exam
The Practice
of Statistics
fifth EDitiON
AP® is a trademark registered by the College Board, which was not involved in the production of, and does not endorse, this product.
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Publisher: Ann heath
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Library of Congress Control Number: 2013949503
ISBN-13: 978-1-4641-0873-0
ISBN-10: 1-4641-0873-0
© 2015, 2012, 2008, 2003, 1999 by W. H. Freeman and Company
First printing 2014
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For the AP® Exam
The Practice fifth EDitiON
of Statistics

Daren S. Starnes
The Lawrenceville School
Josh Tabor
Canyon del Oro High School
Daniel S. Yates
Statistics Consultant
David S. Moore
Purdue University
W. h. freeman and Company/BfW
New York
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Contents
About the Authors vi 5 Probability: What Are the Chances? 286
To the Student xii introduction 288
Overview: What Is Statistics? xxi 5.1 Randomness, Probability, and Simulation 289
5.2 Probability Rules 305
1 Exploring Data xxxii 5.3 Conditional Probability and Independence 318
free Response AP® Problem, Yay! 338
introduction: Data Analysis: Making Sense of Data 2
Chapter 5 Review 338
1.1 Analyzing Categorical Data 7
Chapter 5 Review Exercises 340
1.2 Displaying Quantitative Data with Graphs 25
Chapter 5 AP® Statistics Practice test 342
1.3 Describing Quantitative Data with Numbers 48
free Response AP® Problem, Yay! 74
Chapter 1 Review 74 6 Random Variables 344
Chapter 1 Review Exercises 76
introduction 346
Chapter 1 AP® Statistics Practice test 78
6.1 Discrete and Continuous Random Variables 347
2 Modeling Distributions of Data 82 6.2 Transforming and Combining Random Variables 363
6.3 Binomial and Geometric Random Variables 386
introduction 84 free Response AP® Problem, Yay! 414
2.1 Describing Location in a Distribution 85
Chapter 6 Review 415
2.2 Density Curves and Normal Distributions 103
Chapter 6 Review Exercises 416
free Response AP® Problem, Yay! 134 Chapter 6 AP® Statistics Practice test 418
Chapter 2 Review 134
Chapter 2 Review Exercises 136
Chapter 2 AP® Statistics Practice test 137 7 Sampling Distributions 420
introduction 422
3 Describing Relationships 140
7.1 What Is a Sampling Distribution? 424
introduction 142 7.2 Sample Proportions 440
3.1 Scatterplots and Correlation 143 7.3 Sample Means 450
3.2 Least-Squares Regression 164 free Response AP® Problem, Yay! 464
free Response AP® Problem, Yay! 199 Chapter 7 Review 465
Chapter 3 Review 200 Chapter 7 Review Exercises 466
Chapter 3 Review Exercises 202 Chapter 7 AP® Statistics Practice test 468
Chapter 3 AP® Statistics Practice test 203 Cumulative AP® Practice Test 2 470
4 Designing Studies 206
introduction 208 8 Estimating with Confidence 474
4.1 Sampling and Surveys 209 introduction 476
4.2 Experiments 234 8.1 Confidence Intervals: The Basics 477
4.3 Using Studies Wisely 266 8.2 Estimating a Population Proportion 492
free Response AP® Problem, Yay! 275 8.3 Estimating a Population Mean 507
Chapter 4 Review 276 free Response AP® Problem, Yay! 530
Chapter 4 Review Exercises 278 Chapter 8 Review 531
Chapter 4 AP® Statistics Practice test 279 Chapter 8 Review Exercises 532
Cumulative AP® Practice Test 1 282 Chapter 8 AP® Statistics Practice test 534
iv
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Section 2.1 Scatterplots and Correlations
9 Testing a Claim 536 Additional topics on CD-ROM and at
http://www.whfreeman.com/tps5e
introduction 538
9.1 Significance Tests: The Basics 539 13 Analysis of Variance
9.2 Tests about a Population Proportion 554
14 Multiple Linear Regression
9.3 Tests about a Population Mean 574
free Response AP® Problem, Yay! 601 15 Logistic Regression
Chapter 9 Review 602
Chapter 9 Review Exercises 604 Photo Credits PC-1
Chapter 9 AP® Statistics Practice test 605 Notes and Data Sources N/DS-1
Solutions S-1
10 Comparing Two Populations or Groups 608
Appendices A-1
introduction 610
Appendix A: About the AP® Exam A-1
10.1 Comparing Two Proportions 612
Appendix B: TI-Nspire Technology Corners A-3
10.2 Comparing Two Means 634
free Response AP® Problem, Yay! 662
Formulas for AP® Statistics Exam F-1
Chapter 10 Review 662
Chapter 10 Review Exercises 664 Tables T-1
Chapter 10 AP® Statistics Practice test 666 Table A: Standard Normal Probabilities T-1
Cumulative AP® Practice Test 3 669 Table B: t Distribution Critical Values T-3
Table C: Chi-Square Distribution
Critical Values T-4
11 Inference for Distributions
Table D: Random Digits T-5
of Categorical Data 676
Glossary/Glosario G-1
introduction 678 Index I-1
11.1 Chi-Square Tests for Goodness of Fit 680
11.2 Inference for Two-Way Tables 697
Technology Corners Reference Back Endpaper
free Response AP® Problem, Yay! 730
Inference Summary Back Endpaper
Chapter 11 Review 731
Chapter 11 Review Exercises 732
Chapter 11 AP® Statistics Practice test 734
12 More about Regression 736
introduction 738
12.1 Inference for Linear Regression 739
12.2 Transforming to Achieve Linearity 765
free Response AP® Problem, Yay! 793
Chapter 12 Review 794
Chapter 12 Review Exercises 795
Chapter 12 AP® Statistics Practice test 797
Cumulative AP® Practice Test 4 800
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about the authors
Daren S. StarneS is Mathematics Department Chair and JoSh tabor has enjoyed teaching general and AP® Statistics
holds the Robert S. and Christina Seix Dow Distinguished Master to high school students for more than 18 years, most recently at
Teacher Chair in Mathematics at The Lawrenceville School near his alma mater, Canyon del Oro High School in Oro Valley, Ari-
Princeton, New Jersey. He earned his MA in Mathematics from zona. He received a BS in Mathematics from Biola University, in
the University of Michigan and his BS in Mathematics from the La Mirada, California. In recognition of his outstanding work as
University of North Carolina at Charlotte. Daren is also an alum- an educator, Josh was named one of the five finalists for Arizona
nus of the North Carolina School of Science and Mathematics. Teacher of the Year in 2011. He is a past member of the AP®
Daren has led numerous one-day and weeklong AP® Statistics in- Statistics Development Committee (2005–2009), as well as an ex-
stitutes for new and experienced AP® teachers, and he has been a perienced Table Leader and Question Leader at the AP® Statistics
Reader, Table Leader, and Question Leader for the AP® Statistics Reading. Each year, Josh leads one-week AP® Summer Institutes
exam since 1998. Daren is a frequent speaker at local, state, re- and one-day College Board workshops around the country and
gional, national, and international conferences. For two years, he frequently speaks at local, national, and international conferences.
served as coeditor of the Technology Tips column in the NCTM In addition to teaching and speaking, Josh has authored articles in
journal The Mathematics Teacher. From 2004 to 2009, Daren The Mathematics Teacher, STATS Magazine, and The Journal of
served on the ASA/NCTM Joint Committee on the Curriculum Statistics Education. He is the author of the Annotated Teacher’s
in Statistics and Probability (which he chaired in 2009). While Edition and Teacher’s Resource Materials for The Practice of Sta-
on the committee, he edited the Guidelines for Assessment and tistics 4e and 5e, along with the Solutions Manual for The Practice
Instruction in Statistics Education (GAISE) pre-K–12 report and of Statistics 5e. Combining his love of statistics and love of sports,
coauthored (with Roxy Peck) Making Sense of Statistical Studies, Josh teamed with Christine Franklin to write Statistical Reasoning
a capstone module in statistical thinking for high school students. in Sports, an innovative textbook for on-level statistics courses.
Daren is also coauthor of the popular text Statistics Through
Applications, First and Second Editions.
Daniel S. YateS taught AP® Statistics in the Electronic Class- DaviD S. Moore is Shanti S. Gupta Distinguished Professor of
room (a distance-learning facility) affiliated with Henrico County Statistics (Emeritus) at Purdue University and was 1998 President of
Public Schools in Richmond, Virginia. Prior to high school teach- the American Statistical Association. David is an elected fellow of the
ing, he was on the mathematics faculty at Virginia Tech and American Statistical Association and of the Institute of Mathematical
Randolph-Macon College. He has a PhD in Mathematics Educa- Statistics and an elected member of the International Statistical Insti-
tion from Florida State University. Dan received a College Board/ tute. He has served as program director for statistics and probability
Siemens Foundation Advanced Placement Teaching Award in at the National Science Foundation. He is the author of influential
2000. articles on statistics education and of several leading textbooks.
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